To solve the inequality \( 4 - x < 3x + 2 \), follow these steps:

### Step 1: Move all the terms involving \( x \) to one side.
Start by subtracting \( 3x \) from both sides:
\[
4 - x - 3x < 2
\]
Simplify the left side:
\[
4 - 4x < 2
\]

### Step 2: Move the constant term to the other side.
Now, subtract \( 4 \) from both sides:
\[
-4x < 2 - 4
\]
Simplify:
\[
-4x < -2
\]

### Step 3: Solve for \( x \).
Divide both sides by \( -4 \). Remember, when dividing or multiplying by a negative number in an inequality, the inequality sign flips:
\[
x > \frac{-2}{-4}
\]
Simplify:
\[
x > \frac{1}{2}
\]

### Final Answer:
\[
x > \frac{1}{2}
\]

Would you like more details, or have any questions?

Here are 5 related questions you can explore:
1. Solve \( 2x - 5 < 3x + 7 \).
2. Solve the inequality \( 5x + 3 > 4x - 6 \).
3. How does solving an inequality differ from solving an equation?
4. What happens if you multiply or divide both sides of an inequality by a negative number?
5. Graph the solution \( x > \frac{1}{2} \) on a number line.

**Tip**: Always remember to flip the inequality sign when multiplying or dividing by a negative number!

Learn how to solve the linear inequality 4 - x < 3x + 2 with a clear, step-by-step breakdown. This tutorial covers essential algebraic concepts, including handling inequalities and flipping the inequality sign when dividing by a negative number. Perfect for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation